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Article dans une revue Bullettin of the Gioenia Academy of Natural Sciences of Catania Année : 2023

Many infinities, or only one?

Résumé

In this short note we first account for Aristotle's views on infinity, by clarifying the way his notion of potential infinity should be understood, in the light of his notion of entelechy. We then present four distinct ways in which mathematicians attempted to tame the notion of actual infinity, and we ask the question of whether they are indeed four different ways, or whether they ultimately are variations on the same concept. We suggest that what mathematicians are doing is indeed to find a way to construct a form of actual infinity that subsumes, into itself, the potential infinity, and observe how the presence of the former brings to a different view about potential infinity than Aristotle's.
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Dates et versions

halshs-04386750, version 1 (11-01-2024)

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Giovanna R Giardina, Marco Panza, Daniele Carlo Struppa. Many infinities, or only one?. Bullettin of the Gioenia Academy of Natural Sciences of Catania, 2023, 56 (386), pp.FP28-41. ⟨10.35352/gioenia.v56i386.108⟩. ⟨halshs-04386750⟩
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Dernière date de mise à jour le 28/04/2024
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